This invention relates to convolution function generators and to their utilization in digital filters.
The values of the samples y.sub.n of a signal provided by a filter discretely defined by coefficients h.sub.n and fed by samples x.sub.n of a signal to be filtered are derived from the following convolution relation: ##EQU2## WHICH SHOWS THE NEED FOR CONVOLUTION FUNCTION GENERATORS.
The more obvious manner for building such a device consists in using N+1 multipliers and N adders thus directly performing the operations symbolized by expression (1). However, this is not the least expensive mode, nor the fastest. More especially, the filtering quality relates directly to the value of the parameter N: the greater N is, the better the filtering.
Under such constraints, attempts have been made to build devices requiring less calculation power while giving an equivalent filtering quality. For this purpose, consideration was given to using the properties of certain mathematical transforms among which, one may mention the Fourier transform or the Mersenne transform described by Charles M. Rader in an article entitled: "Discrete Convolution via Mersenne Transforms", published in the "IEEE Transactions on Computers", Vol. C.21, No. 12, December, 1972, pages 1269 to 1273. This Mersenne transform and its inverse show several desirable properties. First of all, term-to-term products in the transform domain correspond to the convolutions in the object domain. Otherwise stated, if X.sub.k and H.sub.k, respectively, are the transforms of the x.sub.n and h.sub.n terms, and if the term-to-term products X.sub.k . H.sub.k = Y.sub.k are carried out, the application of the inverse Mersenne transform to the Y.sub.k's provides the desired y.sub.n's. Thus, the convolution theorem applies to the Mersenne transform. In addition, the transpositions from the object domain to the Mersenne one, and the converse, require only additions and shifts, which shows the reason for the interest taken in a convolution function generator based on the properties of the Mersenne transform.
However, one of the major disadvantages of such a device lies in the fact that it must be able to process words whose size depends on the number of samples x.sub.n and h.sub.n, to which the transforms are applied, thus practically limiting the application of this solution to short convolutions.